Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(45.7782354788\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.210756\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21076 | 0.856134 | 0.428067 | − | 0.903747i | \(-0.359195\pi\) | ||||
0.428067 | + | 0.903747i | \(0.359195\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.534070 | −0.267035 | ||||||||
\(5\) | 2.21076 | 0.988680 | 0.494340 | − | 0.869269i | \(-0.335410\pi\) | ||||
0.494340 | + | 0.869269i | \(0.335410\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.06814 | −1.08475 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.67669 | 0.846442 | ||||||||
\(11\) | 0.789244 | 0.237966 | 0.118983 | − | 0.992896i | \(-0.462037\pi\) | ||||
0.118983 | + | 0.992896i | \(0.462037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.64663 | −0.661657 | ||||||||
\(17\) | −1.74483 | −0.423182 | −0.211591 | − | 0.977358i | \(-0.567865\pi\) | ||||
−0.211591 | + | 0.977358i | \(0.567865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.32331 | −0.991836 | −0.495918 | − | 0.868369i | \(-0.665168\pi\) | ||||
−0.495918 | + | 0.868369i | \(0.665168\pi\) | |||||||
\(20\) | −1.18070 | −0.264012 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.955582 | 0.203731 | ||||||||
\(23\) | 1.11256 | 0.231984 | 0.115992 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115992 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.112558 | −0.0225117 | ||||||||
\(26\) | 1.21076 | 0.237449 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48965 | 1.57649 | 0.788244 | − | 0.615362i | \(-0.210990\pi\) | ||||
0.788244 | + | 0.615362i | \(0.210990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.70041 | −1.02382 | −0.511912 | − | 0.859038i | \(-0.671063\pi\) | ||||
−0.511912 | + | 0.859038i | \(0.671063\pi\) | |||||||
\(32\) | 2.93186 | 0.518284 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.11256 | −0.362301 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27890 | 0.374648 | 0.187324 | − | 0.982298i | \(-0.440019\pi\) | ||||
0.187324 | + | 0.982298i | \(0.440019\pi\) | |||||||
\(38\) | −5.23448 | −0.849144 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.78291 | −1.07247 | ||||||||
\(41\) | 12.1363 | 1.89537 | 0.947684 | − | 0.319209i | \(-0.103417\pi\) | ||||
0.947684 | + | 0.319209i | \(0.103417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.06814 | 1.23038 | 0.615190 | − | 0.788379i | \(-0.289079\pi\) | ||||
0.615190 | + | 0.788379i | \(0.289079\pi\) | |||||||
\(44\) | −0.421512 | −0.0635453 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.34704 | 0.198610 | ||||||||
\(47\) | 8.74483 | 1.27556 | 0.637782 | − | 0.770217i | \(-0.279852\pi\) | ||||
0.637782 | + | 0.770217i | \(0.279852\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.136281 | −0.0192730 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.534070 | −0.0740622 | ||||||||
\(53\) | −7.95558 | −1.09278 | −0.546392 | − | 0.837530i | \(-0.683999\pi\) | ||||
−0.546392 | + | 0.837530i | \(0.683999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74483 | 0.235272 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2789 | 1.34969 | ||||||||
\(59\) | 10.9556 | 1.42630 | 0.713148 | − | 0.701014i | \(-0.247269\pi\) | ||||
0.713148 | + | 0.701014i | \(0.247269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0681 | 1.67320 | 0.836602 | − | 0.547811i | \(-0.184539\pi\) | ||||
0.836602 | + | 0.547811i | \(0.184539\pi\) | |||||||
\(62\) | −6.90180 | −0.876530 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.84302 | 1.10538 | ||||||||
\(65\) | 2.21076 | 0.274211 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.55779 | 0.801162 | 0.400581 | − | 0.916261i | \(-0.368808\pi\) | ||||
0.400581 | + | 0.916261i | \(0.368808\pi\) | |||||||
\(68\) | 0.931860 | 0.113005 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.85738 | −0.695144 | −0.347572 | − | 0.937653i | \(-0.612994\pi\) | ||||
−0.347572 | + | 0.937653i | \(0.612994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00936 | −0.937425 | −0.468712 | − | 0.883351i | \(-0.655282\pi\) | ||||
−0.468712 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(74\) | 2.75919 | 0.320749 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.30895 | 0.264855 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.91116 | −0.777567 | −0.388783 | − | 0.921329i | \(-0.627105\pi\) | ||||
−0.388783 | + | 0.921329i | \(0.627105\pi\) | |||||||
\(80\) | −5.85105 | −0.654167 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.6941 | 1.62269 | ||||||||
\(83\) | 3.14262 | 0.344947 | 0.172473 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172473 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.85738 | −0.418392 | ||||||||
\(86\) | 9.76855 | 1.05337 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.42151 | −0.258134 | ||||||||
\(89\) | 3.39145 | 0.359493 | 0.179747 | − | 0.983713i | \(-0.442472\pi\) | ||||
0.179747 | + | 0.983713i | \(0.442472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.594184 | −0.0619480 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.5878 | 1.09205 | ||||||||
\(95\) | −9.55779 | −0.980609 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0981974 | 0.00997044 | 0.00498522 | − | 0.999988i | \(-0.498413\pi\) | ||||
0.00498522 | + | 0.999988i | \(0.498413\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0601141 | 0.00601141 | ||||||||
\(101\) | 6.90180 | 0.686755 | 0.343378 | − | 0.939197i | \(-0.388429\pi\) | ||||
0.343378 | + | 0.939197i | \(0.388429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8223 | 1.55902 | 0.779510 | − | 0.626390i | \(-0.215468\pi\) | ||||
0.779510 | + | 0.626390i | \(0.215468\pi\) | |||||||
\(104\) | −3.06814 | −0.300856 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.63227 | −0.935569 | ||||||||
\(107\) | 2.02372 | 0.195641 | 0.0978203 | − | 0.995204i | \(-0.468813\pi\) | ||||
0.0978203 | + | 0.995204i | \(0.468813\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3470 | −1.66154 | −0.830772 | − | 0.556612i | \(-0.812101\pi\) | ||||
−0.830772 | + | 0.556612i | \(0.812101\pi\) | |||||||
\(110\) | 2.11256 | 0.201425 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1807 | −0.957720 | −0.478860 | − | 0.877891i | \(-0.658950\pi\) | ||||
−0.478860 | + | 0.877891i | \(0.658950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.45960 | 0.229358 | ||||||||
\(116\) | −4.53407 | −0.420978 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.2645 | 1.22110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3771 | −0.943372 | ||||||||
\(122\) | 15.8223 | 1.43249 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.04442 | 0.273397 | ||||||||
\(125\) | −11.3026 | −1.01094 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4452 | 1.45928 | 0.729639 | − | 0.683832i | \(-0.239688\pi\) | ||||
0.729639 | + | 0.683832i | \(0.239688\pi\) | |||||||
\(128\) | 4.84302 | 0.428067 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.67669 | 0.234761 | ||||||||
\(131\) | 12.3327 | 1.07751 | 0.538755 | − | 0.842462i | \(-0.318895\pi\) | ||||
0.538755 | + | 0.842462i | \(0.318895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.93989 | 0.685902 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.35337 | 0.459048 | ||||||||
\(137\) | 3.34704 | 0.285957 | 0.142978 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142978 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.16634 | 0.523022 | 0.261511 | − | 0.965201i | \(-0.415779\pi\) | ||||
0.261511 | + | 0.965201i | \(0.415779\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.09186 | −0.595136 | ||||||||
\(143\) | 0.789244 | 0.0659999 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.7685 | 1.55864 | ||||||||
\(146\) | −9.69738 | −0.802561 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.21709 | −0.100044 | ||||||||
\(149\) | −18.8367 | −1.54316 | −0.771581 | − | 0.636131i | \(-0.780534\pi\) | ||||
−0.771581 | + | 0.636131i | \(0.780534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1901 | 1.64304 | 0.821522 | − | 0.570177i | \(-0.193125\pi\) | ||||
0.821522 | + | 0.570177i | \(0.193125\pi\) | |||||||
\(152\) | 13.2645 | 1.07590 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.6022 | −1.01223 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8811 | −1.10783 | −0.553916 | − | 0.832572i | \(-0.686867\pi\) | ||||
−0.553916 | + | 0.832572i | \(0.686867\pi\) | |||||||
\(158\) | −8.36773 | −0.665701 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.48163 | 0.512418 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4897 | 0.899939 | 0.449970 | − | 0.893044i | \(-0.351435\pi\) | ||||
0.449970 | + | 0.893044i | \(0.351435\pi\) | |||||||
\(164\) | −6.48163 | −0.506130 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.80494 | 0.295321 | ||||||||
\(167\) | −12.9699 | −1.00364 | −0.501822 | − | 0.864971i | \(-0.667337\pi\) | ||||
−0.501822 | + | 0.864971i | \(0.667337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −4.67035 | −0.358200 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.30895 | −0.328555 | ||||||||
\(173\) | 2.48029 | 0.188573 | 0.0942865 | − | 0.995545i | \(-0.469943\pi\) | ||||
0.0942865 | + | 0.995545i | \(0.469943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.08884 | −0.157452 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.10622 | 0.307774 | ||||||||
\(179\) | 8.15698 | 0.609681 | 0.304841 | − | 0.952403i | \(-0.401397\pi\) | ||||
0.304841 | + | 0.952403i | \(0.401397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.60855 | −0.268221 | −0.134111 | − | 0.990966i | \(-0.542818\pi\) | ||||
−0.134111 | + | 0.990966i | \(0.542818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.41349 | −0.251645 | ||||||||
\(185\) | 5.03808 | 0.370407 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.37709 | −0.100703 | ||||||||
\(188\) | −4.67035 | −0.340620 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.5722 | −0.839532 | ||||||||
\(191\) | −0.337675 | −0.0244333 | −0.0122167 | − | 0.999925i | \(-0.503889\pi\) | ||||
−0.0122167 | + | 0.999925i | \(0.503889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.42151 | 0.606194 | 0.303097 | − | 0.952960i | \(-0.401979\pi\) | ||||
0.303097 | + | 0.952960i | \(0.401979\pi\) | |||||||
\(194\) | 0.118893 | 0.00853603 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.51035 | 0.606337 | 0.303169 | − | 0.952937i | \(-0.401955\pi\) | ||||
0.303169 | + | 0.952937i | \(0.401955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6166 | 1.03614 | 0.518071 | − | 0.855338i | \(-0.326650\pi\) | ||||
0.518071 | + | 0.855338i | \(0.326650\pi\) | |||||||
\(200\) | 0.345345 | 0.0244196 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.35640 | 0.587954 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.8304 | 1.87391 | ||||||||
\(206\) | 19.1570 | 1.33473 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.64663 | −0.183511 | ||||||||
\(209\) | −3.41215 | −0.236023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8667 | −1.64305 | −0.821527 | − | 0.570169i | \(-0.806878\pi\) | ||||
−0.821527 | + | 0.570169i | \(0.806878\pi\) | |||||||
\(212\) | 4.24884 | 0.291811 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.45023 | 0.167495 | ||||||||
\(215\) | 17.8367 | 1.21645 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −21.0030 | −1.42250 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.931860 | −0.0628260 | ||||||||
\(221\) | −1.74483 | −0.117370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.27890 | −0.0856412 | −0.0428206 | − | 0.999083i | \(-0.513634\pi\) | ||||
−0.0428206 | + | 0.999083i | \(0.513634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.3263 | −0.819936 | ||||||||
\(227\) | 9.57849 | 0.635747 | 0.317873 | − | 0.948133i | \(-0.397031\pi\) | ||||
0.317873 | + | 0.948133i | \(0.397031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5134 | 0.892989 | 0.446494 | − | 0.894786i | \(-0.352672\pi\) | ||||
0.446494 | + | 0.894786i | \(0.352672\pi\) | |||||||
\(230\) | 2.97797 | 0.196361 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −26.0474 | −1.71010 | ||||||||
\(233\) | −28.9586 | −1.89714 | −0.948571 | − | 0.316565i | \(-0.897470\pi\) | ||||
−0.948571 | + | 0.316565i | \(0.897470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.3327 | 1.26112 | ||||||||
\(236\) | −5.85105 | −0.380871 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.1363 | 1.56125 | 0.780623 | − | 0.625002i | \(-0.214902\pi\) | ||||
0.780623 | + | 0.625002i | \(0.214902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.92552 | 0.639359 | 0.319680 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319680 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(242\) | −12.5641 | −0.807653 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.97930 | −0.446804 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.32331 | −0.275086 | ||||||||
\(248\) | 17.4897 | 1.11059 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.6847 | −0.865497 | ||||||||
\(251\) | 18.4990 | 1.16765 | 0.583824 | − | 0.811880i | \(-0.301556\pi\) | ||||
0.583824 | + | 0.811880i | \(0.301556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.878080 | 0.0552044 | ||||||||
\(254\) | 19.9112 | 1.24934 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8223 | −0.738895 | ||||||||
\(257\) | 16.6767 | 1.04026 | 0.520132 | − | 0.854086i | \(-0.325883\pi\) | ||||
0.520132 | + | 0.854086i | \(0.325883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.18070 | −0.0732238 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.9319 | 0.922493 | ||||||||
\(263\) | 13.4690 | 0.830531 | 0.415266 | − | 0.909700i | \(-0.363689\pi\) | ||||
0.415266 | + | 0.909700i | \(0.363689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.5878 | −1.08041 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.50232 | −0.213938 | ||||||||
\(269\) | −30.5578 | −1.86314 | −0.931571 | − | 0.363560i | \(-0.881561\pi\) | ||||
−0.931571 | + | 0.363560i | \(0.881561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.22512 | −0.256658 | −0.128329 | − | 0.991732i | \(-0.540961\pi\) | ||||
−0.128329 | + | 0.991732i | \(0.540961\pi\) | |||||||
\(272\) | 4.61791 | 0.280002 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.05244 | 0.244817 | ||||||||
\(275\) | −0.0888361 | −0.00535702 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00000 | −0.180253 | −0.0901263 | − | 0.995930i | \(-0.528727\pi\) | ||||
−0.0901263 | + | 0.995930i | \(0.528727\pi\) | |||||||
\(278\) | 7.46593 | 0.447777 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.27890 | 0.374568 | 0.187284 | − | 0.982306i | \(-0.440032\pi\) | ||||
0.187284 | + | 0.982306i | \(0.440032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.5371 | −1.39914 | −0.699568 | − | 0.714566i | \(-0.746624\pi\) | ||||
−0.699568 | + | 0.714566i | \(0.746624\pi\) | |||||||
\(284\) | 3.12825 | 0.185628 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.955582 | 0.0565047 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9556 | −0.820917 | ||||||||
\(290\) | 22.7241 | 1.33441 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.27756 | 0.250325 | ||||||||
\(293\) | 21.6166 | 1.26285 | 0.631427 | − | 0.775435i | \(-0.282470\pi\) | ||||
0.631427 | + | 0.775435i | \(0.282470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.2201 | 1.41015 | ||||||||
\(296\) | −6.99197 | −0.406400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.8066 | −1.32115 | ||||||||
\(299\) | 1.11256 | 0.0643409 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.4452 | 1.40667 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.4422 | 0.656256 | ||||||||
\(305\) | 28.8905 | 1.65426 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.3945 | 1.16397 | 0.581987 | − | 0.813198i | \(-0.302275\pi\) | ||||
0.581987 | + | 0.813198i | \(0.302275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.2582 | −0.866608 | ||||||||
\(311\) | 12.9492 | 0.734284 | 0.367142 | − | 0.930165i | \(-0.380336\pi\) | ||||
0.367142 | + | 0.930165i | \(0.380336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.2345 | 1.87852 | 0.939262 | − | 0.343201i | \(-0.111511\pi\) | ||||
0.939262 | + | 0.343201i | \(0.111511\pi\) | |||||||
\(314\) | −16.8066 | −0.948453 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.69105 | 0.207638 | ||||||||
\(317\) | 4.87175 | 0.273624 | 0.136812 | − | 0.990597i | \(-0.456314\pi\) | ||||
0.136812 | + | 0.990597i | \(0.456314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.70041 | 0.375151 | ||||||||
\(320\) | 19.5498 | 1.09287 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.54343 | 0.419728 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.112558 | −0.00624362 | ||||||||
\(326\) | 13.9112 | 0.770468 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −37.2358 | −2.05600 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.87175 | 0.377705 | 0.188853 | − | 0.982005i | \(-0.439523\pi\) | ||||
0.188853 | + | 0.982005i | \(0.439523\pi\) | |||||||
\(332\) | −1.67838 | −0.0921129 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.7034 | −0.859254 | ||||||||
\(335\) | 14.4977 | 0.792093 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0712 | 0.603085 | 0.301542 | − | 0.953453i | \(-0.402499\pi\) | ||||
0.301542 | + | 0.953453i | \(0.402499\pi\) | |||||||
\(338\) | 1.21076 | 0.0658564 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.06011 | 0.111725 | ||||||||
\(341\) | −4.49901 | −0.243635 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −24.7542 | −1.33466 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00303 | 0.161444 | ||||||||
\(347\) | −5.62593 | −0.302016 | −0.151008 | − | 0.988533i | \(-0.548252\pi\) | ||||
−0.151008 | + | 0.988533i | \(0.548252\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4783 | −0.989122 | −0.494561 | − | 0.869143i | \(-0.664671\pi\) | ||||
−0.494561 | + | 0.869143i | \(0.664671\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.31395 | 0.123334 | ||||||||
\(353\) | 4.67035 | 0.248578 | 0.124289 | − | 0.992246i | \(-0.460335\pi\) | ||||
0.124289 | + | 0.992246i | \(0.460335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9492 | −0.687275 | ||||||||
\(356\) | −1.81127 | −0.0959974 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.87611 | 0.521968 | ||||||||
\(359\) | 11.7211 | 0.618616 | 0.309308 | − | 0.950962i | \(-0.399903\pi\) | ||||
0.309308 | + | 0.950962i | \(0.399903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.308953 | −0.0162607 | ||||||||
\(362\) | −4.36907 | −0.229633 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.7067 | −0.926813 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.9699 | −1.04242 | −0.521211 | − | 0.853428i | \(-0.674520\pi\) | ||||
−0.521211 | + | 0.853428i | \(0.674520\pi\) | |||||||
\(368\) | −2.94453 | −0.153494 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.09989 | 0.317118 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.42651 | −0.229196 | −0.114598 | − | 0.993412i | \(-0.536558\pi\) | ||||
−0.114598 | + | 0.993412i | \(0.536558\pi\) | |||||||
\(374\) | −1.66732 | −0.0862153 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.8304 | −1.38367 | ||||||||
\(377\) | 8.48965 | 0.437239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.5702 | −1.67302 | −0.836509 | − | 0.547953i | \(-0.815407\pi\) | ||||
−0.836509 | + | 0.547953i | \(0.815407\pi\) | |||||||
\(380\) | 5.10453 | 0.261857 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.408842 | −0.0209182 | ||||||||
\(383\) | 14.1964 | 0.725402 | 0.362701 | − | 0.931906i | \(-0.381855\pi\) | ||||
0.362701 | + | 0.931906i | \(0.381855\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.1964 | 0.518983 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0524443 | −0.00266246 | ||||||||
\(389\) | −17.3170 | −0.878006 | −0.439003 | − | 0.898486i | \(-0.644668\pi\) | ||||
−0.439003 | + | 0.898486i | \(0.644668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.94122 | −0.0981718 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.3040 | 0.519106 | ||||||||
\(395\) | −15.2789 | −0.768765 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.7241 | −0.789171 | −0.394586 | − | 0.918859i | \(-0.629112\pi\) | ||||
−0.394586 | + | 0.918859i | \(0.629112\pi\) | |||||||
\(398\) | 17.6971 | 0.887075 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.297900 | 0.0148950 | ||||||||
\(401\) | −3.57849 | −0.178701 | −0.0893506 | − | 0.996000i | \(-0.528479\pi\) | ||||
−0.0893506 | + | 0.996000i | \(0.528479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.70041 | −0.283958 | ||||||||
\(404\) | −3.68605 | −0.183388 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.79861 | 0.0891536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3501 | 1.55016 | 0.775080 | − | 0.631863i | \(-0.217709\pi\) | ||||
0.775080 | + | 0.631863i | \(0.217709\pi\) | |||||||
\(410\) | 32.4850 | 1.60432 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.45023 | −0.416313 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.94756 | 0.341042 | ||||||||
\(416\) | 2.93186 | 0.143746 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.13128 | −0.202068 | ||||||||
\(419\) | −28.7716 | −1.40558 | −0.702792 | − | 0.711396i | \(-0.748063\pi\) | ||||
−0.702792 | + | 0.711396i | \(0.748063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.190060 | −0.00926297 | −0.00463148 | − | 0.999989i | \(-0.501474\pi\) | ||||
−0.00463148 | + | 0.999989i | \(0.501474\pi\) | |||||||
\(422\) | −28.8968 | −1.40667 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.4088 | 1.18540 | ||||||||
\(425\) | 0.196395 | 0.00952655 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.08081 | −0.0522429 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.5959 | 1.04145 | ||||||||
\(431\) | −25.6734 | −1.23664 | −0.618322 | − | 0.785925i | \(-0.712187\pi\) | ||||
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.82233 | −0.0875755 | −0.0437877 | − | 0.999041i | \(-0.513943\pi\) | ||||
−0.0437877 | + | 0.999041i | \(0.513943\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.26454 | 0.443691 | ||||||||
\(437\) | −4.80994 | −0.230091 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.735465 | −0.0351018 | −0.0175509 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175509 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(440\) | −5.35337 | −0.255212 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.11256 | −0.100484 | ||||||||
\(443\) | 3.71174 | 0.176350 | 0.0881751 | − | 0.996105i | \(-0.471896\pi\) | ||||
0.0881751 | + | 0.996105i | \(0.471896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.49768 | 0.355424 | ||||||||
\(446\) | −1.54843 | −0.0733203 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.17570 | 0.244256 | 0.122128 | − | 0.992514i | \(-0.461028\pi\) | ||||
0.122128 | + | 0.992514i | \(0.461028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.57849 | 0.451033 | ||||||||
\(452\) | 5.43721 | 0.255745 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.5972 | 0.544284 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.1299 | −1.59653 | −0.798266 | − | 0.602305i | \(-0.794249\pi\) | ||||
−0.798266 | + | 0.602305i | \(0.794249\pi\) | |||||||
\(458\) | 16.3614 | 0.764518 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.31360 | −0.0612467 | ||||||||
\(461\) | −11.4008 | −0.530989 | −0.265494 | − | 0.964112i | \(-0.585535\pi\) | ||||
−0.265494 | + | 0.964112i | \(0.585535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.0124 | −1.39479 | −0.697397 | − | 0.716685i | \(-0.745659\pi\) | ||||
−0.697397 | + | 0.716685i | \(0.745659\pi\) | |||||||
\(464\) | −22.4690 | −1.04310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.0618 | −1.62421 | ||||||||
\(467\) | 34.1663 | 1.58103 | 0.790515 | − | 0.612443i | \(-0.209813\pi\) | ||||
0.790515 | + | 0.612443i | \(0.209813\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 23.4072 | 1.07969 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.6133 | −1.54718 | ||||||||
\(473\) | 6.36773 | 0.292789 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.486625 | 0.0223279 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29.2231 | 1.33664 | ||||||||
\(479\) | −12.8761 | −0.588324 | −0.294162 | − | 0.955756i | \(-0.595041\pi\) | ||||
−0.294162 | + | 0.955756i | \(0.595041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.27890 | 0.103909 | ||||||||
\(482\) | 12.0174 | 0.547377 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.54210 | 0.251913 | ||||||||
\(485\) | 0.217091 | 0.00985758 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.9399 | −0.994191 | −0.497096 | − | 0.867696i | \(-0.665600\pi\) | ||||
−0.497096 | + | 0.867696i | \(0.665600\pi\) | |||||||
\(488\) | −40.0949 | −1.81501 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.11256 | −0.185597 | −0.0927986 | − | 0.995685i | \(-0.529581\pi\) | ||||
−0.0927986 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.8130 | −0.667142 | ||||||||
\(494\) | −5.23448 | −0.235510 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.0869 | 0.677420 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0331 | 0.852038 | 0.426019 | − | 0.904714i | \(-0.359916\pi\) | ||||
0.426019 | + | 0.904714i | \(0.359916\pi\) | |||||||
\(500\) | 6.03639 | 0.269956 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.3978 | 0.999662 | ||||||||
\(503\) | −35.8698 | −1.59935 | −0.799677 | − | 0.600430i | \(-0.794996\pi\) | ||||
−0.799677 | + | 0.600430i | \(0.794996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.2582 | 0.678981 | ||||||||
\(506\) | 1.06314 | 0.0472624 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.78291 | −0.389679 | ||||||||
\(509\) | 17.5465 | 0.777733 | 0.388867 | − | 0.921294i | \(-0.372867\pi\) | ||||
0.388867 | + | 0.921294i | \(0.372867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24.0000 | −1.06066 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.1914 | 0.890604 | ||||||||
\(515\) | 34.9793 | 1.54137 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.90180 | 0.303541 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.78291 | −0.297450 | ||||||||
\(521\) | −8.84302 | −0.387420 | −0.193710 | − | 0.981059i | \(-0.562052\pi\) | ||||
−0.193710 | + | 0.981059i | \(0.562052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9112 | −0.958108 | −0.479054 | − | 0.877785i | \(-0.659020\pi\) | ||||
−0.479054 | + | 0.877785i | \(0.659020\pi\) | |||||||
\(524\) | −6.58651 | −0.287733 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3076 | 0.711046 | ||||||||
\(527\) | 9.94622 | 0.433264 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7622 | −0.946183 | ||||||||
\(530\) | −21.2946 | −0.924978 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1363 | 0.525681 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.47396 | 0.193426 | ||||||||
\(536\) | −20.1202 | −0.869061 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.9980 | −1.59510 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8654 | 0.983061 | 0.491530 | − | 0.870860i | \(-0.336438\pi\) | ||||
0.491530 | + | 0.870860i | \(0.336438\pi\) | |||||||
\(542\) | −5.11559 | −0.219733 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.11559 | −0.219329 | ||||||||
\(545\) | −38.3501 | −1.64274 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.2676 | −1.50793 | −0.753966 | − | 0.656913i | \(-0.771862\pi\) | ||||
−0.753966 | + | 0.656913i | \(0.771862\pi\) | |||||||
\(548\) | −1.78755 | −0.0763605 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.107559 | −0.00458632 | ||||||||
\(551\) | −36.7034 | −1.56362 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.63227 | −0.154320 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.29326 | −0.139665 | ||||||||
\(557\) | −39.8698 | −1.68934 | −0.844668 | − | 0.535290i | \(-0.820202\pi\) | ||||
−0.844668 | + | 0.535290i | \(0.820202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.06814 | 0.341246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.60221 | 0.320680 | ||||||||
\(563\) | 25.5972 | 1.07879 | 0.539397 | − | 0.842052i | \(-0.318652\pi\) | ||||
0.539397 | + | 0.842052i | \(0.318652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5070 | −0.946878 | ||||||||
\(566\) | −28.4977 | −1.19785 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.9713 | 0.754058 | ||||||||
\(569\) | 25.0949 | 1.05203 | 0.526016 | − | 0.850475i | \(-0.323685\pi\) | ||||
0.526016 | + | 0.850475i | \(0.323685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.2488 | −1.30772 | −0.653862 | − | 0.756614i | \(-0.726852\pi\) | ||||
−0.653862 | + | 0.756614i | \(0.726852\pi\) | |||||||
\(572\) | −0.421512 | −0.0176243 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.125228 | −0.00522236 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.8717 | 0.535858 | 0.267929 | − | 0.963439i | \(-0.413661\pi\) | ||||
0.267929 | + | 0.963439i | \(0.413661\pi\) | |||||||
\(578\) | −16.8968 | −0.702814 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.0237 | −0.416212 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.27890 | −0.260045 | ||||||||
\(584\) | 24.5738 | 1.01687 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.1724 | 1.08117 | ||||||||
\(587\) | 9.96692 | 0.411379 | 0.205689 | − | 0.978617i | \(-0.434056\pi\) | ||||
0.205689 | + | 0.978617i | \(0.434056\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.6447 | 1.01547 | ||||||||
\(590\) | 29.3246 | 1.20728 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.03139 | −0.247889 | ||||||||
\(593\) | −20.5909 | −0.845566 | −0.422783 | − | 0.906231i | \(-0.638947\pi\) | ||||
−0.422783 | + | 0.906231i | \(0.638947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0601 | 0.412078 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.34704 | 0.0550844 | ||||||||
\(599\) | 12.5371 | 0.512252 | 0.256126 | − | 0.966643i | \(-0.417554\pi\) | ||||
0.256126 | + | 0.966643i | \(0.417554\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.82233 | −0.0743343 | −0.0371672 | − | 0.999309i | \(-0.511833\pi\) | ||||
−0.0371672 | + | 0.999309i | \(0.511833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.7829 | −0.438750 | ||||||||
\(605\) | −22.9412 | −0.932693 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.9780 | 1.25736 | 0.628678 | − | 0.777665i | \(-0.283596\pi\) | ||||
0.628678 | + | 0.777665i | \(0.283596\pi\) | |||||||
\(608\) | −12.6754 | −0.514053 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 34.9793 | 1.41627 | ||||||||
\(611\) | 8.74483 | 0.353778 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4502 | 0.502860 | 0.251430 | − | 0.967875i | \(-0.419099\pi\) | ||||
0.251430 | + | 0.967875i | \(0.419099\pi\) | |||||||
\(614\) | 24.6927 | 0.996518 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.7809 | −1.27945 | −0.639726 | − | 0.768603i | \(-0.720952\pi\) | ||||
−0.639726 | + | 0.768603i | \(0.720952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.22512 | 0.169822 | 0.0849109 | − | 0.996389i | \(-0.472939\pi\) | ||||
0.0849109 | + | 0.996389i | \(0.472939\pi\) | |||||||
\(620\) | 6.73047 | 0.270302 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.6784 | 0.628646 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.4245 | −0.976982 | ||||||||
\(626\) | 40.2388 | 1.60827 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.41349 | 0.295830 | ||||||||
\(629\) | −3.97628 | −0.158545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.31198 | 0.291085 | 0.145543 | − | 0.989352i | \(-0.453507\pi\) | ||||
0.145543 | + | 0.989352i | \(0.453507\pi\) | |||||||
\(632\) | 21.2044 | 0.843467 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.89849 | 0.234259 | ||||||||
\(635\) | 36.3564 | 1.44276 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.11256 | 0.321179 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.7067 | 0.423221 | ||||||||
\(641\) | 23.0474 | 0.910319 | 0.455160 | − | 0.890410i | \(-0.349582\pi\) | ||||
0.455160 | + | 0.890410i | \(0.349582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −48.9379 | −1.92992 | −0.964961 | − | 0.262392i | \(-0.915489\pi\) | ||||
−0.964961 | + | 0.262392i | \(0.915489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.13325 | 0.359343 | ||||||||
\(647\) | 33.4309 | 1.31430 | 0.657152 | − | 0.753758i | \(-0.271761\pi\) | ||||
0.657152 | + | 0.753758i | \(0.271761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.64663 | 0.339410 | ||||||||
\(650\) | −0.136281 | −0.00534537 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.13628 | −0.240315 | ||||||||
\(653\) | 10.4629 | 0.409445 | 0.204723 | − | 0.978820i | \(-0.434371\pi\) | ||||
0.204723 | + | 0.978820i | \(0.434371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.2645 | 1.06531 | ||||||||
\(656\) | −32.1202 | −1.25408 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.73849 | 0.340403 | 0.170202 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170202 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.61354 | −0.179446 | −0.0897230 | − | 0.995967i | \(-0.528598\pi\) | ||||
−0.0897230 | + | 0.995967i | \(0.528598\pi\) | |||||||
\(662\) | 8.32001 | 0.323366 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.64199 | −0.374182 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.44523 | 0.365721 | ||||||||
\(668\) | 6.92686 | 0.268008 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.5531 | 0.678137 | ||||||||
\(671\) | 10.3140 | 0.398166 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.83802 | 0.379228 | 0.189614 | − | 0.981859i | \(-0.439276\pi\) | ||||
0.189614 | + | 0.981859i | \(0.439276\pi\) | |||||||
\(674\) | 13.4045 | 0.516321 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.534070 | −0.0205412 | ||||||||
\(677\) | −4.69541 | −0.180459 | −0.0902296 | − | 0.995921i | \(-0.528760\pi\) | ||||
−0.0902296 | + | 0.995921i | \(0.528760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.8350 | 0.453851 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.44721 | −0.208584 | ||||||||
\(683\) | −11.0207 | −0.421695 | −0.210848 | − | 0.977519i | \(-0.567622\pi\) | ||||
−0.210848 | + | 0.977519i | \(0.567622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.39948 | 0.282720 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.3534 | −0.814090 | ||||||||
\(689\) | −7.95558 | −0.303084 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.7635 | −1.47463 | −0.737317 | − | 0.675546i | \(-0.763908\pi\) | ||||
−0.737317 | + | 0.675546i | \(0.763908\pi\) | |||||||
\(692\) | −1.32465 | −0.0503556 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.81163 | −0.258566 | ||||||||
\(695\) | 13.6323 | 0.517101 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.1757 | −0.802087 | ||||||||
\(698\) | −22.3727 | −0.846820 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0681 | 1.21120 | 0.605598 | − | 0.795770i | \(-0.292934\pi\) | ||||
0.605598 | + | 0.795770i | \(0.292934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.85238 | −0.371590 | ||||||||
\(704\) | 6.97930 | 0.263042 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.65465 | 0.212816 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.3451 | 1.44008 | 0.720040 | − | 0.693933i | \(-0.244124\pi\) | ||||
0.720040 | + | 0.693933i | \(0.244124\pi\) | |||||||
\(710\) | −15.6784 | −0.588399 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.4055 | −0.389961 | ||||||||
\(713\) | −6.34204 | −0.237511 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.74483 | 0.0652528 | ||||||||
\(716\) | −4.35640 | −0.162806 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.1914 | 0.529618 | ||||||||
\(719\) | 8.72413 | 0.325355 | 0.162678 | − | 0.986679i | \(-0.447987\pi\) | ||||
0.162678 | + | 0.986679i | \(0.447987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.374067 | −0.0139213 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.92722 | 0.0716244 | ||||||||
\(725\) | −0.955582 | −0.0354894 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.6754 | 0.989334 | 0.494667 | − | 0.869083i | \(-0.335290\pi\) | ||||
0.494667 | + | 0.869083i | \(0.335290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.4385 | −0.793476 | ||||||||
\(731\) | −14.0775 | −0.520675 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.7211 | 0.986966 | 0.493483 | − | 0.869755i | \(-0.335723\pi\) | ||||
0.493483 | + | 0.869755i | \(0.335723\pi\) | |||||||
\(734\) | −24.1787 | −0.892453 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.26187 | 0.120234 | ||||||||
\(737\) | 5.17570 | 0.190649 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0538 | 1.32626 | 0.663130 | − | 0.748504i | \(-0.269228\pi\) | ||||
0.663130 | + | 0.748504i | \(0.269228\pi\) | |||||||
\(740\) | −2.69069 | −0.0989117 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.96058 | 0.108613 | 0.0543066 | − | 0.998524i | \(-0.482705\pi\) | ||||
0.0543066 | + | 0.998524i | \(0.482705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41.6433 | −1.52569 | ||||||||
\(746\) | −5.35942 | −0.196222 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.735465 | 0.0268913 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.1550 | 1.57475 | 0.787374 | − | 0.616475i | \(-0.211440\pi\) | ||||
0.787374 | + | 0.616475i | \(0.211440\pi\) | |||||||
\(752\) | −23.1443 | −0.843986 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.2789 | 0.374335 | ||||||||
\(755\) | 44.6353 | 1.62444 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.7335 | 0.680880 | 0.340440 | − | 0.940266i | \(-0.389424\pi\) | ||||
0.340440 | + | 0.940266i | \(0.389424\pi\) | |||||||
\(758\) | −39.4345 | −1.43233 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 29.3246 | 1.06372 | ||||||||
\(761\) | 4.22948 | 0.153318 | 0.0766592 | − | 0.997057i | \(-0.475575\pi\) | ||||
0.0766592 | + | 0.997057i | \(0.475575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.180342 | 0.00652456 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.1884 | 0.621041 | ||||||||
\(767\) | 10.9556 | 0.395583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.1299 | −0.761965 | −0.380983 | − | 0.924582i | \(-0.624414\pi\) | ||||
−0.380983 | + | 0.924582i | \(0.624414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.49768 | −0.161875 | ||||||||
\(773\) | −33.0742 | −1.18960 | −0.594798 | − | 0.803875i | \(-0.702768\pi\) | ||||
−0.594798 | + | 0.803875i | \(0.702768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.641629 | 0.0230480 | ||||||||
\(776\) | −0.301284 | −0.0108154 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.9666 | −0.751690 | ||||||||
\(779\) | −52.4690 | −1.87990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.62291 | −0.165421 | ||||||||
\(782\) | −2.35034 | −0.0840482 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.6877 | −1.09529 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.23948 | 0.222413 | 0.111207 | − | 0.993797i | \(-0.464528\pi\) | ||||
0.111207 | + | 0.993797i | \(0.464528\pi\) | |||||||
\(788\) | −4.54512 | −0.161913 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.4990 | −0.658165 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.0681 | 0.464063 | ||||||||
\(794\) | −19.0381 | −0.675636 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.80628 | −0.276686 | ||||||||
\(797\) | 32.1837 | 1.14001 | 0.570003 | − | 0.821643i | \(-0.306942\pi\) | ||||
0.570003 | + | 0.821643i | \(0.306942\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.2582 | −0.539796 | ||||||||
\(800\) | −0.330006 | −0.0116675 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.33268 | −0.152992 | ||||||||
\(803\) | −6.32134 | −0.223075 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.90180 | −0.243106 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.1757 | −0.744958 | ||||||||
\(809\) | −47.8016 | −1.68062 | −0.840308 | − | 0.542109i | \(-0.817626\pi\) | ||||
−0.840308 | + | 0.542109i | \(0.817626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.4957 | −1.31665 | −0.658326 | − | 0.752733i | \(-0.728735\pi\) | ||||
−0.658326 | + | 0.752733i | \(0.728735\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.17767 | 0.0763274 | ||||||||
\(815\) | 25.4008 | 0.889752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.8811 | −1.22034 | ||||||||
\(818\) | 37.9573 | 1.32714 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.3293 | −0.500401 | ||||||||
\(821\) | −39.6447 | −1.38361 | −0.691804 | − | 0.722085i | \(-0.743184\pi\) | ||||
−0.691804 | + | 0.722085i | \(0.743184\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4659 | −0.608824 | −0.304412 | − | 0.952540i | \(-0.598460\pi\) | ||||
−0.304412 | + | 0.952540i | \(0.598460\pi\) | |||||||
\(824\) | −48.5451 | −1.69115 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.53104 | 0.0532396 | 0.0266198 | − | 0.999646i | \(-0.491526\pi\) | ||||
0.0266198 | + | 0.999646i | \(0.491526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.2218 | 1.29277 | 0.646383 | − | 0.763013i | \(-0.276281\pi\) | ||||
0.646383 | + | 0.763013i | \(0.276281\pi\) | |||||||
\(830\) | 8.41179 | 0.291978 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.84302 | 0.306577 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.6734 | −0.992283 | ||||||||
\(836\) | 1.82233 | 0.0630265 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −34.8354 | −1.20337 | ||||||||
\(839\) | −7.37209 | −0.254513 | −0.127256 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127256 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0742 | 1.48532 | ||||||||
\(842\) | −0.230116 | −0.00793034 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.7465 | 0.438753 | ||||||||
\(845\) | 2.21076 | 0.0760523 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 21.0555 | 0.723048 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.237786 | 0.00815600 | ||||||||
\(851\) | 2.53541 | 0.0869126 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.57215 | −0.156548 | −0.0782738 | − | 0.996932i | \(-0.524941\pi\) | ||||
−0.0782738 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.20906 | −0.212221 | ||||||||
\(857\) | −52.0348 | −1.77747 | −0.888737 | − | 0.458417i | \(-0.848416\pi\) | ||||
−0.888737 | + | 0.458417i | \(0.848416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.8905 | −1.46340 | −0.731702 | − | 0.681625i | \(-0.761274\pi\) | ||||
−0.731702 | + | 0.681625i | \(0.761274\pi\) | |||||||
\(860\) | −9.52604 | −0.324835 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.0842 | −1.05873 | ||||||||
\(863\) | 7.82233 | 0.266275 | 0.133138 | − | 0.991098i | \(-0.457495\pi\) | ||||
0.133138 | + | 0.991098i | \(0.457495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.48332 | 0.186438 | ||||||||
\(866\) | −2.20639 | −0.0749763 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.45460 | −0.185034 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.55779 | 0.222202 | ||||||||
\(872\) | 53.2231 | 1.80236 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.82366 | −0.196988 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.7191 | −1.17238 | −0.586191 | − | 0.810173i | \(-0.699373\pi\) | ||||
−0.586191 | + | 0.810173i | \(0.699373\pi\) | |||||||
\(878\) | −0.890468 | −0.0300518 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.61791 | −0.155670 | ||||||||
\(881\) | 11.4422 | 0.385498 | 0.192749 | − | 0.981248i | \(-0.438260\pi\) | ||||
0.192749 | + | 0.981248i | \(0.438260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.0217 | −1.04396 | −0.521982 | − | 0.852956i | \(-0.674807\pi\) | ||||
−0.521982 | + | 0.852956i | \(0.674807\pi\) | |||||||
\(884\) | 0.931860 | 0.0313418 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.49401 | 0.150979 | ||||||||
\(887\) | 12.8304 | 0.430801 | 0.215401 | − | 0.976526i | \(-0.430894\pi\) | ||||
0.215401 | + | 0.976526i | \(0.430894\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.07786 | 0.304291 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.683020 | 0.0228692 | ||||||||
\(893\) | −37.8066 | −1.26515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0331 | 0.602780 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.26651 | 0.209116 | ||||||||
\(899\) | −48.3945 | −1.61405 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.8811 | 0.462447 | ||||||||
\(902\) | 11.5972 | 0.386145 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31.2358 | 1.03889 | ||||||||
\(905\) | −7.97761 | −0.265185 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.1620 | 0.337423 | 0.168711 | − | 0.985665i | \(-0.446039\pi\) | ||||
0.168711 | + | 0.985665i | \(0.446039\pi\) | |||||||
\(908\) | −5.11559 | −0.169767 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.4008 | −1.13975 | −0.569875 | − | 0.821731i | \(-0.693008\pi\) | ||||
−0.569875 | + | 0.821731i | \(0.693008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.48029 | 0.0820856 | ||||||||
\(914\) | −41.3230 | −1.36684 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.21709 | −0.238459 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.15500 | 0.269009 | 0.134504 | − | 0.990913i | \(-0.457056\pi\) | ||||
0.134504 | + | 0.990913i | \(0.457056\pi\) | |||||||
\(920\) | −7.54638 | −0.248797 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.8036 | −0.454598 | ||||||||
\(923\) | −5.85738 | −0.192798 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.256509 | −0.00843396 | ||||||||
\(926\) | −36.3377 | −1.19413 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.8905 | 0.817070 | ||||||||
\(929\) | 4.80994 | 0.157809 | 0.0789045 | − | 0.996882i | \(-0.474858\pi\) | ||||
0.0789045 | + | 0.996882i | \(0.474858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.4659 | 0.506603 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 41.3671 | 1.35357 | ||||||||
\(935\) | −3.04442 | −0.0995631 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.1931 | 1.54173 | 0.770865 | − | 0.636998i | \(-0.219824\pi\) | ||||
0.770865 | + | 0.636998i | \(0.219824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.3250 | −0.336765 | ||||||||
\(941\) | 27.5702 | 0.898762 | 0.449381 | − | 0.893340i | \(-0.351645\pi\) | ||||
0.449381 | + | 0.893340i | \(0.351645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5023 | 0.439696 | ||||||||
\(944\) | −28.9954 | −0.943718 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.70977 | 0.250666 | ||||||||
\(947\) | 27.8698 | 0.905646 | 0.452823 | − | 0.891600i | \(-0.350417\pi\) | ||||
0.452823 | + | 0.891600i | \(0.350417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00936 | −0.259995 | ||||||||
\(950\) | 0.589185 | 0.0191157 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.1076 | 0.878100 | 0.439050 | − | 0.898463i | \(-0.355315\pi\) | ||||
0.439050 | + | 0.898463i | \(0.355315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.746518 | −0.0241567 | ||||||||
\(956\) | −12.8905 | −0.416908 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.5898 | −0.503684 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.49465 | 0.0482146 | ||||||||
\(962\) | 2.75919 | 0.0889598 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.30093 | −0.170731 | ||||||||
\(965\) | 18.6179 | 0.599332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.45657 | −0.143314 | −0.0716568 | − | 0.997429i | \(-0.522829\pi\) | ||||
−0.0716568 | + | 0.997429i | \(0.522829\pi\) | |||||||
\(968\) | 31.8384 | 1.02332 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.262844 | 0.00843940 | ||||||||
\(971\) | −18.9192 | −0.607146 | −0.303573 | − | 0.952808i | \(-0.598180\pi\) | ||||
−0.303573 | + | 0.952808i | \(0.598180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −26.5638 | −0.851161 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.5865 | −1.10709 | ||||||||
\(977\) | −17.4359 | −0.557823 | −0.278911 | − | 0.960317i | \(-0.589974\pi\) | ||||
−0.278911 | + | 0.960317i | \(0.589974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.67669 | 0.0855472 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.97930 | −0.158896 | ||||||||
\(983\) | −15.3815 | −0.490592 | −0.245296 | − | 0.969448i | \(-0.578885\pi\) | ||||
−0.245296 | + | 0.969448i | \(0.578885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.8143 | 0.599473 | ||||||||
\(986\) | −17.9349 | −0.571163 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.30895 | 0.0734576 | ||||||||
\(989\) | 8.97628 | 0.285429 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.42651 | 0.0770807 | 0.0385403 | − | 0.999257i | \(-0.487729\pi\) | ||||
0.0385403 | + | 0.999257i | \(0.487729\pi\) | |||||||
\(992\) | −16.7128 | −0.530632 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.3137 | 1.02441 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0869 | 0.477806 | 0.238903 | − | 0.971043i | \(-0.423212\pi\) | ||||
0.238903 | + | 0.971043i | \(0.423212\pi\) | |||||||
\(998\) | 23.0444 | 0.729458 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5733.2.a.be.1.2 | 3 | ||
3.2 | odd | 2 | 637.2.a.h.1.2 | ✓ | 3 | ||
7.6 | odd | 2 | 5733.2.a.bd.1.2 | 3 | |||
21.2 | odd | 6 | 637.2.e.l.508.2 | 6 | |||
21.5 | even | 6 | 637.2.e.k.508.2 | 6 | |||
21.11 | odd | 6 | 637.2.e.l.79.2 | 6 | |||
21.17 | even | 6 | 637.2.e.k.79.2 | 6 | |||
21.20 | even | 2 | 637.2.a.i.1.2 | yes | 3 | ||
39.38 | odd | 2 | 8281.2.a.bh.1.2 | 3 | |||
273.272 | even | 2 | 8281.2.a.bk.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.h.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
637.2.a.i.1.2 | yes | 3 | 21.20 | even | 2 | ||
637.2.e.k.79.2 | 6 | 21.17 | even | 6 | |||
637.2.e.k.508.2 | 6 | 21.5 | even | 6 | |||
637.2.e.l.79.2 | 6 | 21.11 | odd | 6 | |||
637.2.e.l.508.2 | 6 | 21.2 | odd | 6 | |||
5733.2.a.bd.1.2 | 3 | 7.6 | odd | 2 | |||
5733.2.a.be.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8281.2.a.bh.1.2 | 3 | 39.38 | odd | 2 | |||
8281.2.a.bk.1.2 | 3 | 273.272 | even | 2 |